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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
17.1-a1 17.1-a 5.5.24217.1 \( 17 \) $0$ $\Z/2\Z$ $1$ $477.4099648$ 0.766957533 \( -\frac{1244011801477449574}{17} a^{4} + \frac{918347035277191526}{17} a^{3} + \frac{5597927007057751004}{17} a^{2} - \frac{2807449966148629537}{17} a - \frac{1733261045969695639}{17} \) \( \bigl[a^{4} - 5 a^{2} + 3\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 3\) , \( 1\) , \( 21 a^{4} + 14 a^{3} - 92 a^{2} - 79 a - 22\) , \( 74 a^{4} + 7 a^{3} - 324 a^{2} - 87 a + 12\bigr] \) ${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+{y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-7a-3\right){x}^{2}+\left(21a^{4}+14a^{3}-92a^{2}-79a-22\right){x}+74a^{4}+7a^{3}-324a^{2}-87a+12$
17.1-a2 17.1-a 5.5.24217.1 \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $954.8199297$ 0.766957533 \( -\frac{54226785940}{289} a^{4} + \frac{41617197320}{289} a^{3} + \frac{246699945345}{289} a^{2} - \frac{124059587666}{289} a - \frac{76459531031}{289} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( 3 a^{4} - 2 a^{3} - 14 a^{2} + 6 a + 7\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -28 a^{4} + 14 a^{3} + 124 a^{2} - 21 a - 65\) , \( -92 a^{4} + 50 a^{3} + 410 a^{2} - 78 a - 227\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-14a^{2}+6a+7\right){x}^{2}+\left(-28a^{4}+14a^{3}+124a^{2}-21a-65\right){x}-92a^{4}+50a^{3}+410a^{2}-78a-227$
17.1-a3 17.1-a 5.5.24217.1 \( 17 \) $0$ $\Z/4\Z$ $1$ $1909.639859$ 0.766957533 \( -\frac{171999}{17} a^{4} + \frac{116660}{17} a^{3} + \frac{748638}{17} a^{2} - \frac{385756}{17} a - \frac{232095}{17} \) \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( 2 a^{4} - 9 a^{2} + 2\) , \( 5 a^{4} - 4 a^{3} - 23 a^{2} + 12 a + 9\) , \( 5 a^{4} - 2 a^{3} - 23 a^{2} + 4 a + 5\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+3a+4\right){x}{y}+\left(2a^{4}-9a^{2}+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}^{2}+\left(5a^{4}-4a^{3}-23a^{2}+12a+9\right){x}+5a^{4}-2a^{3}-23a^{2}+4a+5$
17.1-a4 17.1-a 5.5.24217.1 \( 17 \) $0$ $\Z/2\Z$ $1$ $29.83812280$ 0.766957533 \( -\frac{53619990153098106}{83521} a^{4} - \frac{118313872970940038}{83521} a^{3} + \frac{303817425868498660}{83521} a^{2} + \frac{402918681349569873}{83521} a + \frac{102459100667346615}{83521} \) \( \bigl[3 a^{4} - a^{3} - 14 a^{2} + 3 a + 5\) , \( -a^{2} - a + 1\) , \( 0\) , \( -115 a^{4} + 41 a^{3} + 555 a^{2} - 83 a - 318\) , \( -757 a^{4} + 282 a^{3} + 3694 a^{2} - 572 a - 2090\bigr] \) ${y}^2+\left(3a^{4}-a^{3}-14a^{2}+3a+5\right){x}{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-115a^{4}+41a^{3}+555a^{2}-83a-318\right){x}-757a^{4}+282a^{3}+3694a^{2}-572a-2090$
17.2-a1 17.2-a 5.5.24217.1 \( 17 \) $0$ $\Z/2\Z$ $1$ $42.41284946$ 1.090177643 \( \frac{54453237693941353935002949}{83521} a^{4} + \frac{118404470540276106049143231}{83521} a^{3} - \frac{14804571169345841936695190}{83521} a^{2} - \frac{5096744965516204222191469}{4913} a - \frac{25042594099892971051616020}{83521} \) \( \bigl[a^{4} - 5 a^{2} + 3\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 3\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 3 a + 6\) , \( 68 a^{4} - 49 a^{3} - 301 a^{2} + 152 a + 71\) , \( -190 a^{4} + 134 a^{3} + 860 a^{2} - 410 a - 310\bigr] \) ${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+\left(3a^{4}-a^{3}-14a^{2}+3a+6\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-7a-3\right){x}^{2}+\left(68a^{4}-49a^{3}-301a^{2}+152a+71\right){x}-190a^{4}+134a^{3}+860a^{2}-410a-310$
17.2-a2 17.2-a 5.5.24217.1 \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1357.211182$ 1.090177643 \( \frac{1170261661243}{289} a^{4} + \frac{2551882977808}{289} a^{3} - \frac{302825356178}{289} a^{2} - \frac{109434503661}{17} a - \frac{539293780609}{289} \) \( \bigl[a^{4} - 5 a^{2} + 2\) , \( a\) , \( 0\) , \( -260 a^{4} + 96 a^{3} + 1264 a^{2} - 208 a - 704\) , \( -20 a^{4} + 7 a^{3} + 96 a^{2} - 17 a - 54\bigr] \) ${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}={x}^{3}+a{x}^{2}+\left(-260a^{4}+96a^{3}+1264a^{2}-208a-704\right){x}-20a^{4}+7a^{3}+96a^{2}-17a-54$
17.2-a3 17.2-a 5.5.24217.1 \( 17 \) $0$ $\Z/4\Z$ $1$ $2714.422365$ 1.090177643 \( -\frac{153912}{17} a^{4} - \frac{413085}{17} a^{3} - \frac{45051}{17} a^{2} + 25096 a + \frac{175254}{17} \) \( \bigl[a^{4} - 5 a^{2} + 2\) , \( a\) , \( 0\) , \( 65 a^{4} - 24 a^{3} - 316 a^{2} + 52 a + 176\) , \( 0\bigr] \) ${y}^2+\left(a^{4}-5a^{2}+2\right){x}{y}={x}^{3}+a{x}^{2}+\left(65a^{4}-24a^{3}-316a^{2}+52a+176\right){x}$
17.2-a4 17.2-a 5.5.24217.1 \( 17 \) $0$ $\Z/2\Z$ $1$ $678.6055914$ 1.090177643 \( -\frac{8996852763942485}{17} a^{4} - \frac{6501232861661167}{17} a^{3} + \frac{38264452389357430}{17} a^{2} + 2137248783057149 a + \frac{8041904227089956}{17} \) \( \bigl[a^{2} + a - 1\) , \( a\) , \( 0\) , \( -58 a^{4} + 26 a^{3} + 249 a^{2} - 55 a - 147\) , \( 201 a^{4} - 197 a^{3} - 1014 a^{2} + 219 a + 561\bigr] \) ${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-58a^{4}+26a^{3}+249a^{2}-55a-147\right){x}+201a^{4}-197a^{3}-1014a^{2}+219a+561$
23.1-a1 23.1-a 5.5.24217.1 \( 23 \) $1$ $\mathsf{trivial}$ $0.000655576$ $29464.42897$ 1.241254876 \( \frac{2370155}{529} a^{4} + \frac{9772390}{529} a^{3} - \frac{30902810}{529} a^{2} - \frac{40834965}{529} a - \frac{14158252}{529} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( -3 a^{4} + a^{3} + 15 a^{2} - 2 a - 8\) , \( 0\) , \( -2 a^{4} + 2 a^{3} + 10 a^{2} - 2 a - 6\) , \( 17 a^{4} - 6 a^{3} - 81 a^{2} + 13 a + 45\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-3\right){x}{y}={x}^{3}+\left(-3a^{4}+a^{3}+15a^{2}-2a-8\right){x}^{2}+\left(-2a^{4}+2a^{3}+10a^{2}-2a-6\right){x}+17a^{4}-6a^{3}-81a^{2}+13a+45$
29.1-a1 29.1-a 5.5.24217.1 \( 29 \) $0$ $\mathsf{trivial}$ $1$ $205.4596656$ 1.320281099 \( -\frac{3576764830}{29} a^{4} - \frac{6949922095}{29} a^{3} + 85021120 a^{2} + \frac{4914209131}{29} a + \frac{615642891}{29} \) \( \bigl[2 a^{4} - 9 a^{2} + 2\) , \( -2 a^{4} + 9 a^{2} + a - 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 3 a + 3\) , \( -6 a^{4} - 3 a^{3} + 23 a^{2} + 15 a + 1\) , \( -6 a^{4} - 7 a^{3} + 19 a^{2} + 20 a + 4\bigr] \) ${y}^2+\left(2a^{4}-9a^{2}+2\right){x}{y}+\left(2a^{4}-a^{3}-9a^{2}+3a+3\right){y}={x}^{3}+\left(-2a^{4}+9a^{2}+a-1\right){x}^{2}+\left(-6a^{4}-3a^{3}+23a^{2}+15a+1\right){x}-6a^{4}-7a^{3}+19a^{2}+20a+4$
29.1-b1 29.1-b 5.5.24217.1 \( 29 \) $0$ $\mathsf{trivial}$ $1$ $0.436965764$ 0.963122128 \( -\frac{1081740781776866294940863471759}{17249876309} a^{4} + \frac{2120240724895871393224432246770}{17249876309} a^{3} + \frac{43206056991447348862819034032}{594823321} a^{2} - \frac{1374124848200655188432751002870}{17249876309} a - \frac{551901067153896026723504870757}{17249876309} \) \( \bigl[a^{4} - 4 a^{2}\) , \( -3 a^{4} + 14 a^{2} + a - 4\) , \( 2 a^{4} - 9 a^{2} + 2\) , \( 262 a^{4} - 221 a^{3} - 1174 a^{2} + 730 a + 366\) , \( 3311 a^{4} - 2134 a^{3} - 14758 a^{2} + 6316 a + 3956\bigr] \) ${y}^2+\left(a^{4}-4a^{2}\right){x}{y}+\left(2a^{4}-9a^{2}+2\right){y}={x}^{3}+\left(-3a^{4}+14a^{2}+a-4\right){x}^{2}+\left(262a^{4}-221a^{3}-1174a^{2}+730a+366\right){x}+3311a^{4}-2134a^{3}-14758a^{2}+6316a+3956$
29.1-b2 29.1-b 5.5.24217.1 \( 29 \) $0$ $\Z/7\Z$ $1$ $7344.083601$ 0.963122128 \( \frac{8427382}{29} a^{4} + \frac{7718790}{29} a^{3} - 1223286 a^{2} - \frac{41118125}{29} a - \frac{10576765}{29} \) \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 6\) , \( 2 a^{4} - 9 a^{2} + 3\) , \( -a^{4} + 4 a^{2} - 1\) , \( -a^{2} - a\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+3a+4\right){x}{y}+\left(2a^{4}-9a^{2}+3\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-2a-6\right){x}^{2}+\left(-a^{4}+4a^{2}-1\right){x}-a^{2}-a$
37.1-a1 37.1-a 5.5.24217.1 \( 37 \) $0$ $\mathsf{trivial}$ $1$ $233.0926780$ 1.497850472 \( \frac{3031808935}{37} a^{4} - \frac{2191421026}{37} a^{3} - \frac{13575062714}{37} a^{2} + \frac{6780381516}{37} a + \frac{4194484973}{37} \) \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 4\) , \( a^{3} - 4 a\) , \( a^{4} - 4 a^{2} + a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a\) , \( a^{3} - 4 a - 1\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+4a+4\right){x}{y}+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-a^{4}+a^{3}+4a^{2}-3a\right){x}+a^{3}-4a-1$
37.1-b1 37.1-b 5.5.24217.1 \( 37 \) $0$ $\mathsf{trivial}$ $1$ $6.063726461$ 1.052066507 \( -\frac{607404846039294275585}{50653} a^{4} + \frac{224545630126011499990}{50653} a^{3} + \frac{2954014134679662092528}{50653} a^{2} - \frac{484636114530509279215}{50653} a - \frac{1643054132795639869407}{50653} \) \( \bigl[3 a^{4} - a^{3} - 14 a^{2} + 3 a + 5\) , \( 0\) , \( a^{4} - 5 a^{2} + 3\) , \( 7 a^{4} + a^{3} - 36 a^{2} + 2 a\) , \( 27 a^{4} - 141 a^{2} + 20 a + 21\bigr] \) ${y}^2+\left(3a^{4}-a^{3}-14a^{2}+3a+5\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(7a^{4}+a^{3}-36a^{2}+2a\right){x}+27a^{4}-141a^{2}+20a+21$
37.1-b2 37.1-b 5.5.24217.1 \( 37 \) $0$ $\Z/3\Z$ $1$ $1473.485530$ 1.052066507 \( -\frac{5829600}{37} a^{4} + \frac{1892599}{37} a^{3} + \frac{27922132}{37} a^{2} - \frac{4361250}{37} a - \frac{15465165}{37} \) \( \bigl[3 a^{4} - a^{3} - 14 a^{2} + 3 a + 5\) , \( 0\) , \( a^{4} - 5 a^{2} + 3\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 3 a - 5\) , \( -a^{4} + 5 a^{2} - 2\bigr] \) ${y}^2+\left(3a^{4}-a^{3}-14a^{2}+3a+5\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-3a-5\right){x}-a^{4}+5a^{2}-2$
43.1-a1 43.1-a 5.5.24217.1 \( 43 \) $0$ $\mathsf{trivial}$ $1$ $87.59890221$ 1.125818778 \( \frac{370574018535535}{1849} a^{4} + \frac{325399130060553}{1849} a^{3} - \frac{1567138777154508}{1849} a^{2} - \frac{1746670430584042}{1849} a - \frac{422020411508467}{1849} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -2 a^{4} + 9 a^{2} + a - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 2\) , \( 3 a^{4} - 5 a^{3} - 16 a^{2} + 16 a + 11\) , \( -6 a^{4} + a^{3} + 26 a^{2} - 2 a - 9\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-2a-2\right){y}={x}^{3}+\left(-2a^{4}+9a^{2}+a-2\right){x}^{2}+\left(3a^{4}-5a^{3}-16a^{2}+16a+11\right){x}-6a^{4}+a^{3}+26a^{2}-2a-9$
43.1-b1 43.1-b 5.5.24217.1 \( 43 \) $1$ $\mathsf{trivial}$ $0.001395606$ $16404.26636$ 1.471158555 \( -\frac{673276224}{1849} a^{4} + \frac{251558661}{1849} a^{3} + \frac{3275824811}{1849} a^{2} - \frac{548956180}{1849} a - \frac{1829937870}{1849} \) \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( 4 a^{4} - 2 a^{3} - 19 a^{2} + 6 a + 7\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 13 a - 4\) , \( -3 a^{3} - a^{2} + 13 a + 5\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+3a+4\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){y}={x}^{3}+\left(4a^{4}-2a^{3}-19a^{2}+6a+7\right){x}^{2}+\left(-2a^{4}+3a^{3}+9a^{2}-13a-4\right){x}-3a^{3}-a^{2}+13a+5$
47.1-a1 47.1-a 5.5.24217.1 \( 47 \) $1$ $\mathsf{trivial}$ $0.002366304$ $9722.655069$ 1.478411424 \( \frac{2911867}{2209} a^{4} - \frac{42766}{2209} a^{3} - \frac{16302639}{2209} a^{2} - \frac{8533833}{2209} a + \frac{2401431}{2209} \) \( \bigl[a^{4} - 4 a^{2}\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 6 a - 3\) , \( a^{4} - 4 a^{2} + 1\) , \( -4 a^{4} + 3 a^{3} + 17 a^{2} - 11 a - 5\) , \( -3 a^{4} + 2 a^{3} + 13 a^{2} - 7 a - 4\bigr] \) ${y}^2+\left(a^{4}-4a^{2}\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-6a-3\right){x}^{2}+\left(-4a^{4}+3a^{3}+17a^{2}-11a-5\right){x}-3a^{4}+2a^{3}+13a^{2}-7a-4$
53.2-a1 53.2-a 5.5.24217.1 \( 53 \) $1$ $\mathsf{trivial}$ $0.001689072$ $29692.94816$ 1.611429913 \( -\frac{7594719}{53} a^{4} + \frac{15111364}{53} a^{3} + \frac{8390711}{53} a^{2} - \frac{10311463}{53} a - \frac{4105448}{53} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3 a + 4\) , \( a^{4} - 4 a^{2} + 1\) , \( 3 a^{4} - 3 a^{3} - 14 a^{2} + 8 a + 5\) , \( -3 a^{4} + 2 a^{3} + 13 a^{2} - 7 a - 4\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(2a^{4}-a^{3}-10a^{2}+3a+4\right){x}^{2}+\left(3a^{4}-3a^{3}-14a^{2}+8a+5\right){x}-3a^{4}+2a^{3}+13a^{2}-7a-4$
59.1-a1 59.1-a 5.5.24217.1 \( 59 \) $1$ $\mathsf{trivial}$ $0.002977221$ $8328.541854$ 1.593382196 \( -\frac{4479742}{3481} a^{4} + \frac{1301710}{3481} a^{3} + \frac{19202738}{3481} a^{2} - \frac{677371}{3481} a - \frac{7584461}{3481} \) \( \bigl[2 a^{4} - 9 a^{2} + 3\) , \( 4 a^{4} - 2 a^{3} - 19 a^{2} + 6 a + 7\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 3 a + 6\) , \( -4 a^{4} + 3 a^{3} + 18 a^{2} - 9 a - 5\) , \( 3 a^{4} - 2 a^{3} - 13 a^{2} + 7 a + 3\bigr] \) ${y}^2+\left(2a^{4}-9a^{2}+3\right){x}{y}+\left(3a^{4}-a^{3}-14a^{2}+3a+6\right){y}={x}^{3}+\left(4a^{4}-2a^{3}-19a^{2}+6a+7\right){x}^{2}+\left(-4a^{4}+3a^{3}+18a^{2}-9a-5\right){x}+3a^{4}-2a^{3}-13a^{2}+7a+3$
61.1-a1 61.1-a 5.5.24217.1 \( 61 \) $0$ $\mathsf{trivial}$ $1$ $229.4499904$ 1.474442609 \( \frac{27040797}{61} a^{4} + \frac{28132769}{61} a^{3} - \frac{119092723}{61} a^{2} - \frac{136691009}{61} a - \frac{33340058}{61} \) \( \bigl[a\) , \( -5 a^{4} + 2 a^{3} + 24 a^{2} - 5 a - 11\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 4 a + 3\) , \( 7 a^{4} - a^{3} - 34 a^{2} - 2 a + 16\) , \( -2 a^{4} + 3 a^{3} + 11 a^{2} - 12 a - 15\bigr] \) ${y}^2+a{x}{y}+\left(2a^{4}-a^{3}-9a^{2}+4a+3\right){y}={x}^{3}+\left(-5a^{4}+2a^{3}+24a^{2}-5a-11\right){x}^{2}+\left(7a^{4}-a^{3}-34a^{2}-2a+16\right){x}-2a^{4}+3a^{3}+11a^{2}-12a-15$
61.1-b1 61.1-b 5.5.24217.1 \( 61 \) $0$ $\Z/5\Z$ $1$ $4658.517381$ 1.197422848 \( \frac{266240}{61} a^{4} - \frac{512000}{61} a^{3} - \frac{385024}{61} a^{2} + \frac{397312}{61} a + \frac{188416}{61} \) \( \bigl[0\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 5\) , \( a + 1\) , \( -3 a^{4} + 13 a^{2} + 3 a\) , \( a^{3} - 5 a - 2\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-7a-5\right){x}^{2}+\left(-3a^{4}+13a^{2}+3a\right){x}+a^{3}-5a-2$
61.1-b2 61.1-b 5.5.24217.1 \( 61 \) $0$ $\mathsf{trivial}$ $1$ $1.490725562$ 1.197422848 \( \frac{814621975367829286400000}{844596301} a^{4} - \frac{588819537749162764800000}{844596301} a^{3} - \frac{3647503475859398758400000}{844596301} a^{2} + \frac{1821841937334970774327296}{844596301} a + \frac{1127015091876445279977472}{844596301} \) \( \bigl[0\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 3 a + 6\) , \( -172 a^{4} + 72 a^{3} + 808 a^{2} - 126 a - 461\) , \( -1112 a^{4} + 465 a^{3} + 5243 a^{2} - 885 a - 2921\bigr] \) ${y}^2+\left(3a^{4}-a^{3}-14a^{2}+3a+6\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+4a\right){x}^{2}+\left(-172a^{4}+72a^{3}+808a^{2}-126a-461\right){x}-1112a^{4}+465a^{3}+5243a^{2}-885a-2921$
61.1-c1 61.1-c 5.5.24217.1 \( 61 \) $0$ $\mathsf{trivial}$ $1$ $139.6494849$ 0.897385747 \( -\frac{14149720466856}{61} a^{4} + \frac{5230874058759}{61} a^{3} + \frac{68814850746192}{61} a^{2} - \frac{11289779910942}{61} a - \frac{38275551231064}{61} \) \( \bigl[2 a^{4} - 9 a^{2} + 3\) , \( -a^{3} + 3 a\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 4 a + 4\) , \( a^{4} - 2 a^{3} - 6 a^{2} + 7 a + 2\) , \( -2 a^{4} + 4 a^{3} + 7 a^{2} - 13 a - 6\bigr] \) ${y}^2+\left(2a^{4}-9a^{2}+3\right){x}{y}+\left(2a^{4}-a^{3}-9a^{2}+4a+4\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(a^{4}-2a^{3}-6a^{2}+7a+2\right){x}-2a^{4}+4a^{3}+7a^{2}-13a-6$
61.1-d1 61.1-d 5.5.24217.1 \( 61 \) $1$ $\mathsf{trivial}$ $0.002786894$ $17875.95611$ 1.600661755 \( -\frac{31227904}{61} a^{4} + \frac{11927552}{61} a^{3} + \frac{152190976}{61} a^{2} - \frac{26697728}{61} a - \frac{86028288}{61} \) \( \bigl[0\) , \( -2 a^{4} + a^{3} + 10 a^{2} - 2 a - 5\) , \( a^{4} - 4 a^{2} + a + 1\) , \( 4 a^{4} - a^{3} - 18 a^{2} + 2 a + 6\) , \( -2 a^{4} + 8 a^{2} - 2\bigr] \) ${y}^2+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+10a^{2}-2a-5\right){x}^{2}+\left(4a^{4}-a^{3}-18a^{2}+2a+6\right){x}-2a^{4}+8a^{2}-2$
61.2-a1 61.2-a 5.5.24217.1 \( 61 \) $0$ $\Z/5\Z$ $1$ $5294.196281$ 1.360817416 \( -\frac{115152428}{61} a^{4} - \frac{248328657}{61} a^{3} + \frac{38281223}{61} a^{2} + \frac{189872228}{61} a + \frac{54566560}{61} \) \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 3\) , \( 2 a^{4} - 10 a^{2} - a + 4\) , \( a^{2} + a - 2\) , \( 4 a^{4} - 2 a^{3} - 20 a^{2} + 6 a + 9\) , \( 2 a^{4} - 4 a^{3} - 7 a^{2} + 9 a + 4\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+3a+3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(2a^{4}-10a^{2}-a+4\right){x}^{2}+\left(4a^{4}-2a^{3}-20a^{2}+6a+9\right){x}+2a^{4}-4a^{3}-7a^{2}+9a+4$
61.2-a2 61.2-a 5.5.24217.1 \( 61 \) $0$ $\mathsf{trivial}$ $1$ $1.694142810$ 1.360817416 \( \frac{947582806658950190622182}{226981} a^{4} - \frac{684924891007902588272712}{226981} a^{3} - \frac{4242841621501708043901758}{226981} a^{2} + \frac{2119197020585266574178655}{226981} a + \frac{1310965894310847398348250}{226981} \) \( \bigl[a^{4} - 4 a^{2} + a\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 2\) , \( a^{4} - 5 a^{2} + 3\) , \( -33 a^{4} + 86 a^{3} + 225 a^{2} - 86 a - 137\) , \( -317 a^{4} + 1250 a^{3} + 1079 a^{2} - 939 a - 684\bigr] \) ${y}^2+\left(a^{4}-4a^{2}+a\right){x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a+2\right){x}^{2}+\left(-33a^{4}+86a^{3}+225a^{2}-86a-137\right){x}-317a^{4}+1250a^{3}+1079a^{2}-939a-684$
61.2-b1 61.2-b 5.5.24217.1 \( 61 \) $1$ $\mathsf{trivial}$ $0.004171145$ $13410.49608$ 1.797256338 \( -\frac{23855802}{61} a^{4} + \frac{45097325}{61} a^{3} + \frac{29308428}{61} a^{2} - \frac{26625007}{61} a - \frac{11020762}{61} \) \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( 3 a^{4} - 14 a^{2} - a + 3\) , \( a^{4} - 4 a^{2} + a\) , \( a^{4} - 4 a^{3} - 5 a^{2} + 14 a + 9\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 6 a\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+3a+4\right){x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(3a^{4}-14a^{2}-a+3\right){x}^{2}+\left(a^{4}-4a^{3}-5a^{2}+14a+9\right){x}+2a^{4}+a^{3}-10a^{2}-6a$
73.1-a1 73.1-a 5.5.24217.1 \( 73 \) $0$ $\Z/2\Z$ $1$ $532.7413066$ 1.711694302 \( -\frac{13676805271923}{5329} a^{4} + \frac{9479789620397}{5329} a^{3} + \frac{62312937090438}{5329} a^{2} - \frac{30875880058182}{5329} a - \frac{19195743311669}{5329} \) \( \bigl[a^{3} - 3 a\) , \( 2 a^{4} - 9 a^{2} + 1\) , \( a^{2} + a - 2\) , \( -2 a^{4} - 4 a^{3} + 13 a^{2} + 18 a - 18\) , \( -30 a^{4} + 5 a^{3} + 152 a^{2} - 104\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(2a^{4}-9a^{2}+1\right){x}^{2}+\left(-2a^{4}-4a^{3}+13a^{2}+18a-18\right){x}-30a^{4}+5a^{3}+152a^{2}-104$
73.1-a2 73.1-a 5.5.24217.1 \( 73 \) $0$ $\Z/2\Z$ $1$ $1065.482613$ 1.711694302 \( \frac{77128415}{73} a^{4} - \frac{29275704}{73} a^{3} - \frac{374531013}{73} a^{2} + \frac{65385001}{73} a + \frac{205557366}{73} \) \( \bigl[-2 a^{4} + a^{3} + 10 a^{2} - 2 a - 4\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -5 a^{4} + 5 a^{3} + 22 a^{2} - 17 a - 8\) , \( -a^{4} + 4 a^{2} + a\bigr] \) ${y}^2+\left(-2a^{4}+a^{3}+10a^{2}-2a-4\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-7a-3\right){x}^{2}+\left(-5a^{4}+5a^{3}+22a^{2}-17a-8\right){x}-a^{4}+4a^{2}+a$
73.1-b1 73.1-b 5.5.24217.1 \( 73 \) $1$ $\Z/2\Z$ $0.013585443$ $16315.17680$ 1.780391264 \( \frac{25541025}{73} a^{4} - \frac{10499403}{73} a^{3} - \frac{123078275}{73} a^{2} + \frac{24749415}{73} a + \frac{65407672}{73} \) \( \bigl[-a^{4} + 5 a^{2} + a - 1\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 5\) , \( -a^{4} + 5 a^{2} + a - 1\) , \( -2 a^{4} + 9 a^{2} - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}+a-1\right){x}{y}+\left(-a^{4}+5a^{2}+a-1\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-2a-5\right){x}^{2}+\left(-2a^{4}+9a^{2}-2\right){x}+a^{4}-a^{3}-5a^{2}+2a+4$
73.1-b2 73.1-b 5.5.24217.1 \( 73 \) $1$ $\Z/2\Z$ $0.027170887$ $4078.794201$ 1.780391264 \( \frac{897914919792598}{5329} a^{4} - \frac{325870982359061}{5329} a^{3} - \frac{4373494381863622}{5329} a^{2} + \frac{691699015294266}{5329} a + \frac{2451613630132198}{5329} \) \( \bigl[-a^{4} + 5 a^{2} + a - 1\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 5\) , \( -a^{4} + 5 a^{2} + a - 1\) , \( -22 a^{4} + 10 a^{3} + 104 a^{2} - 20 a - 57\) , \( 68 a^{4} - 24 a^{3} - 329 a^{2} + 46 a + 178\bigr] \) ${y}^2+\left(-a^{4}+5a^{2}+a-1\right){x}{y}+\left(-a^{4}+5a^{2}+a-1\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-2a-5\right){x}^{2}+\left(-22a^{4}+10a^{3}+104a^{2}-20a-57\right){x}+68a^{4}-24a^{3}-329a^{2}+46a+178$
83.1-a1 83.1-a 5.5.24217.1 \( 83 \) $0$ $\mathsf{trivial}$ $1$ $271.3468725$ 1.743671421 \( -\frac{42220647154}{83} a^{4} + \frac{18556175594}{83} a^{3} + \frac{202112507761}{83} a^{2} - \frac{45696285762}{83} a - \frac{103175812742}{83} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( -4 a^{4} + a^{3} + 19 a^{2} - 2 a - 6\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 3 a + 6\) , \( -8 a^{4} + 2 a^{3} + 37 a^{2} - 4 a - 10\) , \( -6 a^{4} + 2 a^{3} + 27 a^{2} - 3 a - 9\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){x}{y}+\left(3a^{4}-a^{3}-14a^{2}+3a+6\right){y}={x}^{3}+\left(-4a^{4}+a^{3}+19a^{2}-2a-6\right){x}^{2}+\left(-8a^{4}+2a^{3}+37a^{2}-4a-10\right){x}-6a^{4}+2a^{3}+27a^{2}-3a-9$
83.1-b1 83.1-b 5.5.24217.1 \( 83 \) $1$ $\mathsf{trivial}$ $0.008082099$ $7474.806304$ 1.941037777 \( -\frac{16580520558}{83} a^{4} + \frac{32496792993}{83} a^{3} + \frac{19208593327}{83} a^{2} - \frac{21061708508}{83} a - \frac{8461196561}{83} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 1\) , \( a^{3} - 3 a - 1\) , \( -12 a^{4} - 6 a^{3} + 52 a^{2} + 36 a + 6\) , \( 21 a^{4} + 20 a^{3} - 89 a^{2} - 105 a - 26\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-4a+1\right){x}^{2}+\left(-12a^{4}-6a^{3}+52a^{2}+36a+6\right){x}+21a^{4}+20a^{3}-89a^{2}-105a-26$
83.1-c1 83.1-c 5.5.24217.1 \( 83 \) $1$ $\mathsf{trivial}$ $0.901669351$ $0.685289757$ 1.945617474 \( -\frac{1059382013228619221572682927247070754}{736365263311636486061599129} a^{4} + \frac{2076414215077956021875977058309950102}{736365263311636486061599129} a^{3} + \frac{1227082340350165006565171062239335310}{736365263311636486061599129} a^{2} - \frac{1345722272615370392506917877231739167}{736365263311636486061599129} a - \frac{540496562267508012147668315035311817}{736365263311636486061599129} \) \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( a^{2} + a - 1\) , \( -39 a^{4} + 29 a^{3} + 175 a^{2} - 93 a - 113\) , \( -50 a^{4} + 54 a^{3} + 221 a^{2} - 215 a - 280\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+4a+3\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){x}^{2}+\left(-39a^{4}+29a^{3}+175a^{2}-93a-113\right){x}-50a^{4}+54a^{3}+221a^{2}-215a-280$
83.1-c2 83.1-c 5.5.24217.1 \( 83 \) $1$ $\Z/7\Z$ $0.128809907$ $11517.66496$ 1.945617474 \( \frac{42524487344}{6889} a^{4} - \frac{30725914013}{6889} a^{3} - \frac{190396186538}{6889} a^{2} + \frac{95047801032}{6889} a + \frac{58785346324}{6889} \) \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( a^{2} + a - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( -a^{3} - a^{2} + 3 a + 2\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+4a+3\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){x}^{2}+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){x}-a^{3}-a^{2}+3a+2$
83.2-a1 83.2-a 5.5.24217.1 \( 83 \) $1$ $\mathsf{trivial}$ $0.041991250$ $716.3209315$ 1.932886150 \( -\frac{3205321}{6889} a^{4} + \frac{3829196}{6889} a^{3} + \frac{15699250}{6889} a^{2} - \frac{11133632}{6889} a - \frac{5984717}{6889} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( 2 a^{4} - 10 a^{2} - a + 3\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 3 a + 5\) , \( 3 a^{4} - 3 a^{3} - 13 a^{2} + 10 a + 8\) , \( a^{4} - 5 a^{2}\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){x}{y}+\left(3a^{4}-a^{3}-14a^{2}+3a+5\right){y}={x}^{3}+\left(2a^{4}-10a^{2}-a+3\right){x}^{2}+\left(3a^{4}-3a^{3}-13a^{2}+10a+8\right){x}+a^{4}-5a^{2}$
85.1-a1 85.1-a 5.5.24217.1 \( 5 \cdot 17 \) $0$ $\mathsf{trivial}$ $1$ $203.4472801$ 1.307349536 \( -\frac{678563267}{85} a^{4} + \frac{253885391}{85} a^{3} + \frac{3292945167}{85} a^{2} - \frac{31894747}{5} a - \frac{1831244214}{85} \) \( \bigl[a^{4} - 4 a^{2}\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 6\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( -31 a^{4} + 10 a^{3} + 150 a^{2} - 19 a - 81\) , \( -59 a^{4} + 21 a^{3} + 287 a^{2} - 44 a - 160\bigr] \) ${y}^2+\left(a^{4}-4a^{2}\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+1\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-2a-6\right){x}^{2}+\left(-31a^{4}+10a^{3}+150a^{2}-19a-81\right){x}-59a^{4}+21a^{3}+287a^{2}-44a-160$
85.1-b1 85.1-b 5.5.24217.1 \( 5 \cdot 17 \) $0$ $\mathsf{trivial}$ $1$ $2.635355148$ 1.371715349 \( \frac{83224382820957527}{24565} a^{4} + \frac{73316509594092944}{24565} a^{3} - \frac{352208628542010067}{24565} a^{2} - \frac{23104266017644843}{1445} a - \frac{94916633847261271}{24565} \) \( \bigl[1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 7 a + 5\) , \( a^{4} - 4 a^{2} + 1\) , \( -182 a^{4} + 70 a^{3} + 883 a^{2} - 144 a - 489\) , \( -1350 a^{4} + 501 a^{3} + 6548 a^{2} - 1077 a - 3642\bigr] \) ${y}^2+{x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+7a+5\right){x}^{2}+\left(-182a^{4}+70a^{3}+883a^{2}-144a-489\right){x}-1350a^{4}+501a^{3}+6548a^{2}-1077a-3642$
85.1-b2 85.1-b 5.5.24217.1 \( 5 \cdot 17 \) $0$ $\Z/3\Z$ $1$ $640.3913011$ 1.371715349 \( \frac{7625258}{2125} a^{4} + \frac{7955226}{2125} a^{3} - \frac{33370843}{2125} a^{2} - \frac{2334587}{125} a - \frac{9844789}{2125} \) \( \bigl[-2 a^{4} + a^{3} + 10 a^{2} - 2 a - 5\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 3 a + 6\) , \( a^{2} + a - 1\) , \( 4 a^{4} - 19 a^{2} - 3 a + 9\) , \( 4 a^{4} - a^{3} - 19 a^{2} + a + 8\bigr] \) ${y}^2+\left(-2a^{4}+a^{3}+10a^{2}-2a-5\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(3a^{4}-a^{3}-14a^{2}+3a+6\right){x}^{2}+\left(4a^{4}-19a^{2}-3a+9\right){x}+4a^{4}-a^{3}-19a^{2}+a+8$
85.2-a1 85.2-a 5.5.24217.1 \( 5 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $346.8383044$ 1.114389183 \( -\frac{62677552}{425} a^{4} + \frac{90221181}{425} a^{3} + \frac{148784492}{425} a^{2} - \frac{70726799}{425} a - \frac{76071034}{425} \) \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 4\) , \( 3 a^{4} - 2 a^{3} - 14 a^{2} + 5 a + 7\) , \( 0\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 3 a + 6\) , \( 0\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+4a+4\right){x}{y}={x}^{3}+\left(3a^{4}-2a^{3}-14a^{2}+5a+7\right){x}^{2}+\left(2a^{4}-a^{3}-9a^{2}+3a+6\right){x}$
85.2-a2 85.2-a 5.5.24217.1 \( 5 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $346.8383044$ 1.114389183 \( \frac{332100987110154}{1445} a^{4} - \frac{641864431345097}{1445} a^{3} - \frac{405783721341489}{1445} a^{2} + \frac{419172695961983}{1445} a + \frac{181943957339298}{1445} \) \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 4\) , \( 3 a^{4} - 2 a^{3} - 14 a^{2} + 5 a + 7\) , \( 0\) , \( -8 a^{4} + 4 a^{3} + 36 a^{2} - 12 a - 24\) , \( -34 a^{4} + 13 a^{3} + 154 a^{2} - 33 a - 90\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+4a+4\right){x}{y}={x}^{3}+\left(3a^{4}-2a^{3}-14a^{2}+5a+7\right){x}^{2}+\left(-8a^{4}+4a^{3}+36a^{2}-12a-24\right){x}-34a^{4}+13a^{3}+154a^{2}-33a-90$
85.2-b1 85.2-b 5.5.24217.1 \( 5 \cdot 17 \) $1$ $\Z/2\Z$ $0.007549410$ $16285.02719$ 1.975064959 \( -\frac{102640958}{425} a^{4} + \frac{58128349}{425} a^{3} + \frac{509229993}{425} a^{2} - \frac{171001971}{425} a - \frac{338930961}{425} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 3 a - 6\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( 5 a^{4} - 4 a^{3} - 23 a^{2} + 11 a + 7\) , \( 8 a^{4} - 5 a^{3} - 37 a^{2} + 14 a + 14\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-3a-6\right){x}^{2}+\left(5a^{4}-4a^{3}-23a^{2}+11a+7\right){x}+8a^{4}-5a^{3}-37a^{2}+14a+14$
85.2-b2 85.2-b 5.5.24217.1 \( 5 \cdot 17 \) $1$ $\Z/2\Z$ $0.015098821$ $8142.513599$ 1.975064959 \( \frac{185066934807448}{1445} a^{4} - \frac{87464764407119}{1445} a^{3} - \frac{909727616081443}{1445} a^{2} + \frac{231799410298786}{1445} a + \frac{559295724774971}{1445} \) \( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 3 a - 6\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -50 a^{4} + 26 a^{3} + 232 a^{2} - 74 a - 103\) , \( 65 a^{4} - 10 a^{3} - 330 a^{2} - 4 a + 225\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-3a-6\right){x}^{2}+\left(-50a^{4}+26a^{3}+232a^{2}-74a-103\right){x}+65a^{4}-10a^{3}-330a^{2}-4a+225$
97.1-a1 97.1-a 5.5.24217.1 \( 97 \) $0$ $\Z/4\Z$ $1$ $2396.428605$ 0.962463661 \( -\frac{761279}{97} a^{4} - \frac{433426}{97} a^{3} + \frac{3272354}{97} a^{2} + \frac{2641857}{97} a + \frac{440084}{97} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{4} - 4 a^{2} + a\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 10 a - 5\) , \( -a^{2} - a - 1\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-2a^{4}+2a^{3}+9a^{2}-10a-5\right){x}-a^{2}-a-1$
97.1-a2 97.1-a 5.5.24217.1 \( 97 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $299.5535756$ 0.962463661 \( -\frac{2699246979785}{9409} a^{4} - \frac{2388620148409}{9409} a^{3} + \frac{11413457143722}{9409} a^{2} + \frac{12792778212781}{9409} a + \frac{3119261293489}{9409} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{4} - 4 a^{2} + a\) , \( 13 a^{4} + 22 a^{3} - 51 a^{2} - 110 a - 45\) , \( 72 a^{4} + 75 a^{3} - 298 a^{2} - 393 a - 125\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(13a^{4}+22a^{3}-51a^{2}-110a-45\right){x}+72a^{4}+75a^{3}-298a^{2}-393a-125$
97.1-a3 97.1-a 5.5.24217.1 \( 97 \) $0$ $\Z/2\Z$ $1$ $9.361049240$ 0.962463661 \( \frac{298244004312035170314}{88529281} a^{4} - \frac{224778495680070789765}{88529281} a^{3} - \frac{1183654637007985475374}{88529281} a^{2} + \frac{271982011051561202569}{88529281} a + \frac{648707452832843494777}{88529281} \) \( \bigl[a + 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 4 a + 2\) , \( a^{4} - 4 a^{2} + a\) , \( 5 a^{4} + 5 a^{3} - 25 a^{2} - 21 a - 5\) , \( 222 a^{4} - 145 a^{3} - 1003 a^{2} + 419 a + 280\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(2a^{4}-a^{3}-9a^{2}+4a+2\right){x}^{2}+\left(5a^{4}+5a^{3}-25a^{2}-21a-5\right){x}+222a^{4}-145a^{3}-1003a^{2}+419a+280$
97.1-a4 97.1-a 5.5.24217.1 \( 97 \) $0$ $\Z/2\Z$ $1$ $37.44419696$ 0.962463661 \( -\frac{59222861174558797002}{97} a^{4} - \frac{52003291912703292187}{97} a^{3} + \frac{250450480086938815342}{97} a^{2} + \frac{279142148582207331991}{97} a + \frac{67444715102322126455}{97} \) \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 2\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 2 a + 4\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( -242 a^{4} + 89 a^{3} + 1173 a^{2} - 192 a - 659\) , \( -1145 a^{4} + 417 a^{3} + 5555 a^{2} - 907 a - 3091\bigr] \) ${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-2\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){y}={x}^{3}+\left(3a^{4}-a^{3}-14a^{2}+2a+4\right){x}^{2}+\left(-242a^{4}+89a^{3}+1173a^{2}-192a-659\right){x}-1145a^{4}+417a^{3}+5555a^{2}-907a-3091$
97.2-a1 97.2-a 5.5.24217.1 \( 97 \) $0$ $\Z/2\Z$ $1$ $973.0101957$ 1.563137668 \( -\frac{112934}{97} a^{4} - \frac{488086}{97} a^{3} + \frac{952762}{97} a^{2} + \frac{2083783}{97} a - \frac{1584511}{97} \) \( \bigl[2 a^{4} - 9 a^{2} + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{2} + a - 2\) , \( -a^{4} - 2 a^{3} + 4 a^{2} + 7 a\) , \( -3 a^{4} + 14 a^{2} + a - 7\bigr] \) ${y}^2+\left(2a^{4}-9a^{2}+2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}^{2}+\left(-a^{4}-2a^{3}+4a^{2}+7a\right){x}-3a^{4}+14a^{2}+a-7$
97.2-a2 97.2-a 5.5.24217.1 \( 97 \) $0$ $\Z/2\Z$ $1$ $486.5050978$ 1.563137668 \( -\frac{211331850803}{9409} a^{4} + \frac{1178190929357}{9409} a^{3} - \frac{169653841657}{9409} a^{2} - \frac{4645433005313}{9409} a + \frac{3537886246640}{9409} \) \( \bigl[2 a^{4} - 9 a^{2} + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{2} + a - 2\) , \( -31 a^{4} + 8 a^{3} + 149 a^{2} - 13 a - 80\) , \( -110 a^{4} + 39 a^{3} + 534 a^{2} - 81 a - 295\bigr] \) ${y}^2+\left(2a^{4}-9a^{2}+2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}^{2}+\left(-31a^{4}+8a^{3}+149a^{2}-13a-80\right){x}-110a^{4}+39a^{3}+534a^{2}-81a-295$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.